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Error analysis of supremizer pressure recovery for POD based reduced-order models of the time-dependent Navier-Stokes equations. (English) Zbl 1447.65080
In reduced-order modeling of incompressible flows, the divergence-free property causes the pressure term to drop out of the ROM formulation, leading to a velocity-only ROM. In this paper, the stability and convergence of momentum equation recovery (MER) approach is analyzed for recovering the pressure from a velocity-only reduced-order model (ROM) generated via a proper orthogonal decomposition. The MER method does not require any boundary conditions, however, it does not work universally. Its reliability depends on the classical inf-sup condition, as well as an a priori computable constant dependent on the angle between the initial POD velocity space and supremizer space. The MER approach is compared with the popular solving the pressure Poisson equation (PPE) approach. The performance of the PPE and the MER formulations are compared for pressure recovery on problems with flow between offset cylinders and lid driven cavity. It is shown for the same number of basis functions, the MER approach yields more accurate solutions for the pressure than the PPE method, when the Neumann boundary condition is present.

MSC:
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids
35Q30 Navier-Stokes equations
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
Software:
FEniCS; SyFi
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